1. Due to globalisation, trade and transport, the spread of alien species is increasing dramatically. Some alien species become ecologically harmful by threatening native biota. This can lead to irreversible changes in local biodiversity and ecosystem functioning, and, ultimately, to biotic homogenisation. 2. We risk-assessed all alien plants, animals, fungi and algae, within certain delimitations, that are known to reproduce in Norway. Mainland Norway and the Arctic archipelago of Svalbard plus Jan Mayen were treated as separate assessment areas. Assessments followed the Generic Ecological Impact Assessment of Alien Species (GEIAA) protocol, which uses a fully quantitative set of criteria. 3. A total of 1519 species were risk-assessed, of which 1183 were species reproducing in mainland Norway. Among these, 9% were assessed to have a severe impact, 7% high impact, 7% potentially high impact, and 49% low impact, whereas 29% had no known impact. In Svalbard, 16 alien species were reproducing, one of which with a severe impact. 4. The impact assessments also covered 319 so-called door-knockers, i.e. species that are likely to establish in Norway within 50 years, and 12 regionally alien species. Of the door-knockers, 8% and 10% were assessed to have a severe and high impact, respectively. 5. The impact category of most species was driven by negative interactions with native species, transformation of threatened ecosystems, or genetic contamination. The proportion of alien species with high or severe impact varied significantly across the different pathways of introduction, taxonomic groups, time of introduction, and the environments colonised, but not across continents of origin. 6. Given the large number of alien species reproducing in Norway and the preponderance of species with low impact, it is neither realistic nor necessary to eradicate all of them. Our results can guide management authorities in two ways. First, the use of quantitative assessment criteria facilitates the prioritisation of management resources across species. Second, the background information collected for each species, such as introduction pathways, area of occupancy and ecosystems affected, helps designing appropriate management measures.